Question

Which expression is equivalent to Cosine (StartFraction pi Over 2 EndFraction r) for all values of r?.

Answer 1

The expression that is equivalent to $Cos(\frac{\pi }{2}+r )$ is $-Sinr$.

Given trigonometric expression is:

$Cos(\frac{\pi }{2}+r )$

What is the value of $Cos(\frac{\pi }{2}+\theta )$?

The value of $Cos(\frac{\pi }{2}+\theta )$ is $-Sin\theta$ because $\frac{\pi }{2} +\theta$ lies in the second quadrant and the cosine function is negative in the second quadrant.

So, $Cos(\frac{\pi }{2}+r )= -Sin r$

The range of sine and cosine functions is the same i.e. [-1,1].

Both the functions are periodic functions with periods 2π.

Hence, the expression that is equivalent to $Cos(\frac{\pi }{2}+r )$ is $-Sinr$.

To get more about trigonometric functions visit:

brainly.com/question/2193113